Final Assignment
how does martial status effect hotels choices
Importing data from original databse consumer class variable is created from the variablessrchadultscountand srchchildrencount. Consumers with asrchadultcountof 1 and 2 would be transformed to “sin-gle person” and “couples” respectively. Consumers with a srchchildrencount greater than 1 wouldbe called ”parents”. All other consumers are called ”others
loading and saving
load(file = "../Data/mydata.RData")
# save(mydata,file = "../Data/mydata.RData")
mydata <- data
remove(data)trim database
# mydata <- subset(mydata, select = -c(prop_brand_bool) )
# mydata <- subset(mydata, select = -c(position) )
# mydata <- subset(mydata, select = -c(srch_saturday_night_bool) )
# mydata <- subset(mydata, select = -c(random_bool) )
# mydata <- subset(mydata, select = -c(price_usd_normalized) )
# mydata <- subset(mydata, select = -c(Pclass) )
# mydata <- subset(mydata, select = -c(score) )subsetting
mydata <- mydata[which(mydata$click_bool == 1),]
mydata <- mydata[which(mydata$prop_review_score != 0),]
mydata <- mydata[which(mydata$srch_id < 4000),]
# mydata <- head(mydata,1000)
length(((mydata$srch_id)))## [1] 2611length((unique(mydata$srch_id)))## [1] 2360how many uniqe search ids
pairs plot
df <- subset(head(mydata,50), select = -c(consumer))
pairs(df)
qqnorm(mydata$price_usd)
shapiro.test(mydata$price_usd)##
## Shapiro-Wilk normality test
##
## data: mydata$price_usd
## W = 0.76229, p-value < 2.2e-16not normally disterbuted
library(outliers)
chisq.out.test(mydata$price_usd, variance = var(mydata$price_usd),opposite = TRUE)##
## chi-squared test for outlier
##
## data: mydata$price_usd
## X-squared = 1.8554, p-value = 0.1732
## alternative hypothesis: lowest value 12.8 is an outlierchisq.out.test(mydata$price_usd, variance = var(mydata$price_usd),opposite = FALSE)##
## chi-squared test for outlier
##
## data: mydata$price_usd
## X-squared = 121.28, p-value < 2.2e-16
## alternative hypothesis: highest value 1242 is an outlierremoving outliers
mydata <- mydata[which(mydata$price_usd < 1242 ),]
chisq.out.test(mydata$price_usd, variance = var(mydata$price_usd),opposite = TRUE)##
## chi-squared test for outlier
##
## data: mydata$price_usd
## X-squared = 1.9331, p-value = 0.1644
## alternative hypothesis: lowest value 12.8 is an outlierchisq.out.test(mydata$price_usd, variance = var(mydata$price_usd),opposite = FALSE)##
## chi-squared test for outlier
##
## data: mydata$price_usd
## X-squared = 77.699, p-value < 2.2e-16
## alternative hypothesis: highest value 1002.82 is an outlierlibrary(plotly)## Loading required package: ggplot2##
## Attaching package: 'plotly'## The following object is masked from 'package:ggplot2':
##
## last_plot## The following object is masked from 'package:stats':
##
## filter## The following object is masked from 'package:graphics':
##
## layoutlibrary(ggplot2)
p <- plot_ly(x = mydata$price_usd, type = "histogram")
ggplotly(p)par(mfrow=c(3,2));
qqnorm(mydata$price_usd,main="price_usd")
qqnorm(mydata$prop_starrating,main="prop_starrating")
qqnorm(mydata$prop_review_score,main="prop_review_score")
qqnorm(mydata$prop_location_score1,main="prop_location_score1")
qqnorm(mydata$prop_location_score2,main="prop_location_score2")
par(mfrow=c(3,2));
hist(mydata$price_usd,main="price_usd")
hist(mydata$prop_starrating,main="prop_starrating")
hist(mydata$prop_review_score,main="prop_review_score")
hist(mydata$prop_location_score1,main="prop_location_score1")
hist(mydata$prop_location_score2,main="prop_location_score2")
df <- subset(mydata, select = -c(consumer,click_bool,srch_id,site_id,prop_id))
round(cor(df),3)## prop_starrating prop_review_score
## prop_starrating 1.000 0.424
## prop_review_score 0.424 1.000
## prop_location_score1 0.284 0.095
## prop_location_score2 0.018 0.004
## price_usd 0.502 0.329
## promotion_flag 0.144 -0.019
## booking_bool -0.057 0.027
## prop_location_score1 prop_location_score2 price_usd
## prop_starrating 0.284 0.018 0.502
## prop_review_score 0.095 0.004 0.329
## prop_location_score1 1.000 0.279 0.269
## prop_location_score2 0.279 1.000 0.057
## price_usd 0.269 0.057 1.000
## promotion_flag 0.152 0.005 -0.060
## booking_bool -0.070 0.069 -0.172
## promotion_flag booking_bool
## prop_starrating 0.144 -0.057
## prop_review_score -0.019 0.027
## prop_location_score1 0.152 -0.070
## prop_location_score2 0.005 0.069
## price_usd -0.060 -0.172
## promotion_flag 1.000 0.047
## booking_bool 0.047 1.000 prop_starrating prop_review_score prop_location_score1 prop_location_score2 price_usd promotion_flag booking_boolprop_starrating 1.00 0.31 0.30 0.05 0.47 0.19 0.00 prop_review_score 0.31 1.00 0.15 0.04 0.22 0.06 0.12 prop_location_score1 0.30 0.15 1.00 0.29 0.27 0.16 0.00 prop_location_score2 0.05 0.04 0.29 1.00 0.02 0.03 0.11 price_usd 0.47 0.22 0.27 0.02 1.00 -0.01 -0.11 promotion_flag 0.19 0.06 0.16 0.03 -0.01 1.00 0.11 booking_bool 0.00 0.12 0.00 0.11 -0.11 0.11 1.00
with 0.47 prop_starrating has the highest colinearity with price_usd followed by 0.31 for prop_starrating and prop_review_score
randomized block design
xtabs(price_usd ~ prop_starrating + consumer ,data=mydata)## consumer
## prop_starrating couple other Parents single
## 1 283.27 0.00 0.00 71.00
## 2 14137.50 3322.21 2472.32 6026.93
## 3 70900.22 14139.67 7777.78 26433.55
## 4 97350.56 21189.41 12108.00 39897.67
## 5 41575.44 8771.48 5074.91 13921.75xtabs(price_usd ~ prop_starrating + prop_review_score ,data=mydata)## prop_review_score
## prop_starrating 1 1.5 2 2.5 3 3.5
## 1 0.00 0.00 0.00 71.00 0.00 187.94
## 2 94.00 130.00 602.96 2557.00 4836.28 7592.06
## 3 54.00 241.20 258.23 842.83 6289.98 20924.98
## 4 77.46 96.14 302.71 253.01 2007.35 14835.05
## 5 0.00 0.00 0.00 0.00 290.75 1369.09
## prop_review_score
## prop_starrating 4 4.5 5
## 1 0.00 0.00 95.33
## 2 7519.50 2366.98 260.18
## 3 48109.98 38167.51 4362.51
## 4 67381.06 79444.55 6148.31
## 5 10287.25 47696.34 9700.15attach(mydata)
# par(mfrow=c(3,3))
boxplot(price_usd~prop_starrating); boxplot(price_usd~consumer) ; boxplot(price_usd~prop_review_score) 
interaction.plot(prop_starrating,consumer,price_usd); interaction.plot(consumer,prop_starrating,price_usd) ; interaction.plot(prop_review_score,prop_starrating,price_usd) 
mydata$prop_starrating=factor(mydata$prop_starrating)
mydata$prop_review_score=factor(mydata$prop_review_score)
aovpen=lm(price_usd~prop_starrating+prop_review_score,data=mydata)
anova(aovpen)## Analysis of Variance Table
##
## Response: price_usd
## Df Sum Sq Mean Sq F value Pr(>F)
## prop_starrating 4 6891830 1722958 263.075 < 2.2e-16 ***
## prop_review_score 8 654198 81775 12.486 < 2.2e-16 ***
## Residuals 2597 17008542 6549
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(aovpen)##
## Call:
## lm(formula = price_usd ~ prop_starrating + prop_review_score,
## data = mydata)
##
## Residuals:
## Min 1Q Median 3Q Max
## -218.34 -44.54 -14.29 27.88 689.93
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 41.344 61.947 0.667 0.5046
## prop_starrating2 4.234 40.845 0.104 0.9174
## prop_starrating3 24.803 40.731 0.609 0.5426
## prop_starrating4 72.390 40.767 1.776 0.0759 .
## prop_starrating5 169.608 41.022 4.135 3.67e-05 ***
## prop_review_score1.5 10.668 57.228 0.186 0.8521
## prop_review_score2 28.720 51.858 0.554 0.5797
## prop_review_score2.5 20.780 48.161 0.431 0.6662
## prop_review_score3 35.156 47.245 0.744 0.4569
## prop_review_score3.5 33.086 46.899 0.705 0.4806
## prop_review_score4 44.191 46.815 0.944 0.3453
## prop_review_score4.5 67.388 46.840 1.439 0.1504
## prop_review_score5 101.942 47.524 2.145 0.0320 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 80.93 on 2597 degrees of freedom
## Multiple R-squared: 0.3073, Adjusted R-squared: 0.3041
## F-statistic: 96.02 on 12 and 2597 DF, p-value: < 2.2e-16drop1(aovpen,test="Chisq")## Single term deletions
##
## Model:
## price_usd ~ prop_starrating + prop_review_score
## Df Sum of Sq RSS AIC Pr(>Chi)
## <none> 17008542 22947
## prop_starrating 4 4564659 21573201 23560 < 2.2e-16 ***
## prop_review_score 8 654198 17662741 23030 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1qqnorm(residuals(aovpen))
plot(fitted(aovpen),residuals(aovpen))
prop_starrating is more significant than consumer type and prop_review_score but also both significant
Logistic Regression
An experiment with: an outcome Y that is 0 or 1 (“binary dependent variable”); one or more numerical explanatory variables X1,…,Xp. one or more factor explanatory variables. (“independent variable”). The purpose is to explain Y by a function of X.
# tot=xtabs(~prop_review_score+price_usd,data=mydata);
# hist(mydata$price_usd,main="price_usd");
# round(xtabs(booking_bool~prop_review_score+price_usd,data=mydata)/tot,2)
#
# totage=xtabs(~prop_review_score,data=mydata)
# barplot(xtabs(booking_bool~prop_review_score,data=mydata)/totage)
#
# mydata$prop_review_score2 <- mydata$prop_review_score^2
# myglm=glm(booking_bool~prop_review_score+prop_review_score2+price_usd,data=mydata,family=binomial)
# summary(myglm)myglm=glm(booking_bool~
prop_starrating
+prop_review_score
+prop_location_score1
+prop_location_score2
+price_usd
+promotion_flag
+consumer
,data=mydata,family=binomial)
summary(myglm)##
## Call:
## glm(formula = booking_bool ~ prop_starrating + prop_review_score +
## prop_location_score1 + prop_location_score2 + price_usd +
## promotion_flag + consumer, family = binomial, data = mydata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9877 -1.2780 0.7871 0.9419 2.2879
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.3931195 1.6996472 -1.408 0.159128
## prop_starrating2 2.0123613 1.1719039 1.717 0.085948 .
## prop_starrating3 1.8186350 1.1688833 1.556 0.119738
## prop_starrating4 1.8553442 1.1701929 1.586 0.112852
## prop_starrating5 2.0271625 1.1799129 1.718 0.085785 .
## prop_review_score1.5 -0.7377834 1.6520493 -0.447 0.655173
## prop_review_score2 0.9377906 1.3552031 0.692 0.488942
## prop_review_score2.5 1.2259385 1.2684957 0.966 0.333819
## prop_review_score3 0.7297695 1.2435368 0.587 0.557305
## prop_review_score3.5 1.3953167 1.2354380 1.129 0.258725
## prop_review_score4 1.7001720 1.2332443 1.379 0.168013
## prop_review_score4.5 1.7227357 1.2340611 1.396 0.162718
## prop_review_score5 1.5845126 1.2522512 1.265 0.205753
## prop_location_score1 -0.0897714 0.0307003 -2.924 0.003454 **
## prop_location_score2 1.3253697 0.2705760 4.898 9.67e-07 ***
## price_usd -0.0043143 0.0005711 -7.554 4.23e-14 ***
## promotion_flag 0.2115738 0.0962113 2.199 0.027874 *
## consumerother 0.0894607 0.1374709 0.651 0.515201
## consumerParents -0.0270289 0.1655778 -0.163 0.870329
## consumersingle 0.3819815 0.1050033 3.638 0.000275 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3442.2 on 2609 degrees of freedom
## Residual deviance: 3278.5 on 2590 degrees of freedom
## AIC: 3318.5
##
## Number of Fisher Scoring iterations: 4drop1(myglm,test="Chisq")## Single term deletions
##
## Model:
## booking_bool ~ prop_starrating + prop_review_score + prop_location_score1 +
## prop_location_score2 + price_usd + promotion_flag + consumer
## Df Deviance AIC LRT Pr(>Chi)
## <none> 3278.5 3318.5
## prop_starrating 4 3284.7 3316.7 6.151 0.188168
## prop_review_score 8 3315.3 3339.3 36.792 1.257e-05 ***
## prop_location_score1 1 3287.1 3325.1 8.592 0.003377 **
## prop_location_score2 1 3303.8 3341.8 25.332 4.826e-07 ***
## price_usd 1 3341.6 3379.6 63.067 1.998e-15 ***
## promotion_flag 1 3283.4 3321.4 4.875 0.027250 *
## consumer 3 3292.7 3326.7 14.193 0.002654 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1myglm=glm(booking_bool~
prop_review_score
+prop_location_score1
+prop_location_score2
+price_usd
+promotion_flag
+consumer
,data=mydata,family=binomial)
summary(myglm)##
## Call:
## glm(formula = booking_bool ~ prop_review_score + prop_location_score1 +
## prop_location_score2 + price_usd + promotion_flag + consumer,
## family = binomial, data = mydata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9782 -1.2881 0.7901 0.9427 2.2252
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.5089489 1.2359990 -0.412 0.680507
## prop_review_score1.5 -0.7238342 1.6527538 -0.438 0.661418
## prop_review_score2 0.9868408 1.3573111 0.727 0.467192
## prop_review_score2.5 1.2568074 1.2699084 0.990 0.322329
## prop_review_score3 0.7441285 1.2467621 0.597 0.550608
## prop_review_score3.5 1.3632721 1.2391255 1.100 0.271250
## prop_review_score4 1.6587396 1.2369201 1.341 0.179913
## prop_review_score4.5 1.6905400 1.2376793 1.366 0.171972
## prop_review_score5 1.5343434 1.2556226 1.222 0.221716
## prop_location_score1 -0.0920050 0.0302119 -3.045 0.002324 **
## prop_location_score2 1.2830149 0.2686645 4.776 1.79e-06 ***
## price_usd -0.0041031 0.0005139 -7.985 1.41e-15 ***
## promotion_flag 0.2190510 0.0944278 2.320 0.020353 *
## consumerother 0.0929271 0.1373123 0.677 0.498560
## consumerParents -0.0220893 0.1652853 -0.134 0.893684
## consumersingle 0.3807132 0.1048163 3.632 0.000281 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3442.2 on 2609 degrees of freedom
## Residual deviance: 3284.7 on 2594 degrees of freedom
## AIC: 3316.7
##
## Number of Fisher Scoring iterations: 4drop1(myglm,test="Chisq")## Single term deletions
##
## Model:
## booking_bool ~ prop_review_score + prop_location_score1 + prop_location_score2 +
## price_usd + promotion_flag + consumer
## Df Deviance AIC LRT Pr(>Chi)
## <none> 3284.7 3316.7
## prop_review_score 8 3322.5 3338.5 37.891 7.884e-06 ***
## prop_location_score1 1 3294.0 3324.0 9.316 0.002271 **
## prop_location_score2 1 3308.7 3338.7 24.016 9.555e-07 ***
## price_usd 1 3355.6 3385.6 70.994 < 2.2e-16 ***
## promotion_flag 1 3290.1 3320.1 5.431 0.019781 *
## consumer 3 3298.8 3324.8 14.097 0.002776 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mydata$consumer=factor(mydata$consumer)
mydata$prop_review_score=factor(mydata$prop_review_score)
myglm=glm(booking_bool~
prop_review_score
+prop_location_score2
+price_usd
+promotion_flag
+consumer
,data=mydata,family=binomial)
summary(myglm)##
## Call:
## glm(formula = booking_bool ~ prop_review_score + prop_location_score2 +
## price_usd + promotion_flag + consumer, family = binomial,
## data = mydata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9566 -1.3009 0.8048 0.9368 2.2769
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.625446 1.231149 -0.508 0.611440
## prop_review_score1.5 -0.814697 1.648238 -0.494 0.621106
## prop_review_score2 0.906527 1.352144 0.670 0.502579
## prop_review_score2.5 1.230928 1.265531 0.973 0.330724
## prop_review_score3 0.728006 1.242430 0.586 0.557907
## prop_review_score3.5 1.309675 1.234693 1.061 0.288813
## prop_review_score4 1.614361 1.232521 1.310 0.190262
## prop_review_score4.5 1.639964 1.233256 1.330 0.183589
## prop_review_score5 1.510766 1.251291 1.207 0.227291
## prop_location_score2 1.050305 0.254956 4.120 3.8e-05 ***
## price_usd -0.004498 0.000503 -8.943 < 2e-16 ***
## promotion_flag 0.167049 0.092677 1.802 0.071469 .
## consumerother 0.076274 0.136896 0.557 0.577409
## consumerParents -0.004631 0.164779 -0.028 0.977580
## consumersingle 0.382782 0.104743 3.654 0.000258 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3442.2 on 2609 degrees of freedom
## Residual deviance: 3294.0 on 2595 degrees of freedom
## AIC: 3324
##
## Number of Fisher Scoring iterations: 4drop1(myglm,test="Chisq")## Single term deletions
##
## Model:
## booking_bool ~ prop_review_score + prop_location_score2 + price_usd +
## promotion_flag + consumer
## Df Deviance AIC LRT Pr(>Chi)
## <none> 3294.0 3324.0
## prop_review_score 8 3330.9 3344.9 36.934 1.184e-05 ***
## prop_location_score2 1 3311.7 3339.7 17.682 2.611e-05 ***
## price_usd 1 3384.7 3412.7 90.688 < 2.2e-16 ***
## promotion_flag 1 3297.2 3325.2 3.271 0.070501 .
## consumer 3 3308.1 3332.1 14.138 0.002723 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(c(0,coef(myglm)[2:9]),type="l",main = "coefficients for prop reviews 1 to 5 with 0.5 steps" )
drop1(myglm,test="Chisq")## Single term deletions
##
## Model:
## booking_bool ~ prop_review_score + prop_location_score2 + price_usd +
## promotion_flag + consumer
## Df Deviance AIC LRT Pr(>Chi)
## <none> 3294.0 3324.0
## prop_review_score 8 3330.9 3344.9 36.934 1.184e-05 ***
## prop_location_score2 1 3311.7 3339.7 17.682 2.611e-05 ***
## price_usd 1 3384.7 3412.7 90.688 < 2.2e-16 ***
## promotion_flag 1 3297.2 3325.2 3.271 0.070501 .
## consumer 3 3308.1 3332.1 14.138 0.002723 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1